manual derivatives done using the definition 45 videos
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Derivatives of Exponential Functions
Calculus The Derivative
How to use the definition of the derivative to find a derivative formula for exponential functions.
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The Definition of the Derivative
Calculus The Derivative
How to define the derivative of a function at a point x=a.
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Computing Definite Integrals using Substitution
Calculus The Definite Integral
How to evaluate definite integrals using the method of substitution.
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The Derivative Function
Calculus The Derivative
How to define the derivative function f'(x).
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Derivatives of Polynomial Functions
Calculus The Derivative
How to compute the derivative of a polynomial function using two properties of the derivative.
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Derivatives of Power Functions
Calculus The Derivative
How to determine the derivative of a power function.
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Derivative Notation
Calculus The Derivative
How to recognize and use Newton's and Leibniz's notation for the derivative.
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Derivatives of Logarithmic Functions
Calculus The Derivative
How to infer the derivative of the natural log function using a calculator investigation.
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Derivatives of Linear Functions
Calculus The Derivative
How to determine the derivative of a linear function.
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Definite Integrals and Area
Calculus The Definite Integral
How to use definite integrals to find the area between a curve or under a curve.
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Definition of Antiderivatives
Calculus Antiderivatives and Differential Equations
How to define an antiderivative.
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Optimization Using the First Derivative Test
Calculus Applications of the Derivative
How to evaluate the limit of a function as x goes to infinity (or minus infinity), and how to determine the horizontal asymptote of its graph.
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Optimization Using the Second Derivative Test
Calculus Applications of the Derivative
How to compute the average velocity of an object moving in one dimension from a graph of its position vs. time.
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Definite Integrals As Net Change
Calculus The Definite Integral
How to use the fundamental theorem of calculus to compute the net change of a quantity.
definite integral net change rate of change net change theorem fundamental theorem of calculus -
Curve Sketching with Derivatives
Calculus Applications of the Derivative
How to evaluate the limit of a function using continuity.
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The Fundamental Theorem of Calculus
Calculus The Definite Integral
How to use the fundamental theorem of calculus to evaluate a definite integral.
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Approximating Area Using Rectangles
Calculus The Definite Integral
How to approximate the area under a curve using rectangles.
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The First Derivative Test for Relative Maximum and Minimum
Calculus Applications of the Derivative
How to use an algebraic approach to find one-sided limits of a rational function, and how these limits can be used to find a vertical asymptote.
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Definition of Indefinite Integrals
Calculus Antiderivatives and Differential Equations
How to define an indefinite integral.
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Antidifferentiation
Calculus Antiderivatives and Differential Equations
How to find an antiderivative of a function.
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